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 A365341 a(n) = (5*n)!/(4*n+1)!. 7
 1, 1, 10, 210, 6840, 303600, 17100720, 1168675200, 93963542400, 8691104822400, 909171781056000, 106137499051584000, 13679492361575040000, 1929327666754295808000, 295570742023171270656000, 48877281133334949335040000, 8677556868736487617966080000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..16. FORMULA E.g.f.: exp( 1/5 * Sum_{k>=1} binomial(5*k,k) * x^k/k ). - Seiichi Manyama, Feb 08 2024 a(n) = A000142(n)*A002294(n). - Alois P. Heinz, Feb 08 2024 From Seiichi Manyama, Aug 31 2024: (Start) E.g.f. satisfies A(x) = 1/(1 - x*A(x)^4). a(n) = Sum_{k=0..n} (4*n+1)^(k-1) * |Stirling1(n,k)|. (End) PROG (PARI) a(n) = (5*n)!/(4*n+1)!; (Python) from sympy import ff def A365341(n): return ff(5*n, n-1) # Chai Wah Wu, Sep 01 2023 CROSSREFS Cf. A001761, A001763, A052795, A365340. Cf. A004343. Cf. A000142, A002294. Sequence in context: A120596 A238467 A254322 * A327411 A112364 A201621 Adjacent sequences: A365338 A365339 A365340 * A365342 A365343 A365344 KEYWORD nonn,easy AUTHOR Seiichi Manyama, Sep 01 2023 STATUS approved

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Last modified September 16 23:59 EDT 2024. Contains 375984 sequences. (Running on oeis4.)